Determine the scale factor used in the dilation of line A B, with a center point of dilation at the origin.
(1 point)
The scale factor is
A( -6 , 8)
A ( - 3 , 5 )
B ( 2, - 4)
B ( 4 , -8
The scale factor is determined by the ratio of the lengths of the corresponding sides of the image and the pre-image.
Let's find the lengths of line AB in both the pre-image and image.
In the pre-image:
A( -6, 8) and B( 2, -4)
The length of AB in the pre-image is √((-6-2)^2 + (8-(-4))^2) = √((-8)^2 + (12)^2) = √(64 + 144) = √208
In the image:
A(-3, 5) and B(4, -8)
The length of AB in the image is √((-3-4)^2 + (5-(-8))^2) = √((-7)^2 + (13)^2) = √(49 + 169) = √218
The scale factor is the ratio of the lengths of the corresponding sides:
Scale factor = (length of AB in the image) / (length of AB in the pre-image)
= √218 / √208
Thus, the scale factor used in the dilation of line AB is √218 / √208.